A multiple-beam CLEAN for imaging intra-day variable radio sources

Abstract

The CLEAN algorithm, widely used in radio interferometry for the deconvolution of radio images, performs well only if the raw radio image (dirty image) is, to good approximation, a simple convolution between the instrumental point-spread function (dirty beam) and the true distribution of emission across the sky. An important case in which this approximation breaks down is during frequency synthesis if the observing bandwidth is wide enough for variations in the spectrum of the sky to become significant. The convolution assumption also breaks down, in any situation but snapshot observations, if sources in the field vary significantly in flux density over the duration of the observation. Such time-variation can even be instrumental in nature, for example due to jitter or rotation of the primary beam pattern on the sky during an observation. An algorithm already exists for dealing with the spectral variation encountered in wide-band frequency synthesis interferometry. This algorithm is an extension of CLEAN in which, at each iteration, a set of N "dirty beams" are fitted and subtracted in parallel, instead of just a single dirty beam as in standard CLEAN. In the wide-band algorithm the beams are obtained by expanding a nominal source spectrum in a Taylor series, each term of the series generating one of the beams. In the present paper this algorithm is extended to images which contain sources which vary over both frequency and time. Different expansion schemes (or bases) on the time and frequency axes are compared, and issues such as Gibbs ringing and non-orthogonality are discussed. It is shown that practical considerations make it often desirable to orthogonalize the set of beams before commencing the cleaning. This is easily accomplished via a Gram-Schmidt technique.

Radio interferometric imaging of spatial structure that varies with time and frequency

“…5 in that it does not suffer from instabilities incurred when there is significant overlap between sampled spatial-frequencies. It suggests the choice of N p + N q − 1 basis functions instead of the N p × N q , and also folds-in multi-scale support in a way that allows a wide choice of spatial basis functions whose amplitudes are given by time and frequency polynomials.…”

“…A similar idea applies to time-variability as well, and recent work 5 has demonstrated combined time and frequency modeling for point-sources (without multi-scale support), mainly for the purpose of eliminating artifacts from images of the average intensity distribution. This paper presents a reworking of the system of equations being solved when modeling time and frequency varying structure, and includes multi-scale support.…”

Radio Continuum Surveys with Square Kilometre Array Pathfinders

“…see Stewart, Fenech, & Muxlow 2011). Therefore, characterising the variability and abundance of known radio sources is a necessity for planning future surveys and calibration strategies.…”

Uncertainty quantification for radio interferometric imaging – I. Proximal MCMC methods

“…Classical imaging techniques were developed in the field to solve the RI reconstruction problem, such as CLEAN and its multiscale variants (Högbom 1974;Bhatnagar & Corwnell 2004;Cornwell 2008;Stewart et al 2011). In particular, CLEAN builds a model image by iteratively removing point source components from the residuals of the acquired data (at each iteration).…”